Interference of Light—Undulatory Theory of Light—Propagation of
Light—Newton’s Rings—Measurement of the Length of the Waves of Light,
and of the Frequency of the Vibrations of Ether for each
Colour—Newton’s Scale of Colours—Diffraction of Light—Sir John
Herschel’s Theory of the Absorption of Light—Refraction and Reflection
of Light.
NEWTON and most of his immediate successors imagined light to be a
material substance, emitted by all self-luminous bodies in extremely
minute particles, moving in straight lines with prodigious velocity,
which, by impinging upon the optic nerves, produce the sensation of
light. Many of the observed phenomena have been explained by this
theory; it is, however, totally inadequate to account for the following
circumstances.
When two equal rays of red light, proceeding from two luminous points,
fall upon a sheet of white paper in a dark room, they produce a red spot
on it which will be twice as bright as either ray would produce singly,
provided the difference in the lengths of the two beams, from the
luminous points to the red spot on the paper, be exactly the 0·0000258th
part of an inch. The same effect will take place if the difference in
the lengths be twice, three times, four times, &c., that quantity. But
if the difference in the lengths of the two rays be equal to one-half of
the 0·0000258th part of an inch, or to its 1-1/2, 2-1/2, 3-1/2, &c.,
part, the one light will entirely extinguish the other, and will produce
absolute darkness on the paper where the united beams fall. If the
difference in the lengths of their paths be equal to the 1-1/4, 2-1/4,
3-1/4, &c., of the 0·0000258th part of an inch, the red spot arising
from the combined beams will be of the same intensity which one alone
would produce. If violet light be employed, the difference in the
lengths of the two beams must be equal to the 0·0000157th part of an
inch, in order to produce the same phenomena; and for the other colours,
the difference must be intermediate between the 0·0000258th and the
0·0000157th part of an inch. Similar phenomena may be seen by viewing
the flame of a candle through two very fine slits in a card extremely
near to one another (N. 198); or by admitting the sun’s light into a
dark room through a pin-hole about the fortieth of an inch in diameter,
receiving the image on a sheet of white paper, and holding a slender
wire in the light. Its shadow will be found to consist of a bright white
bar or stripe in the middle, with a series of alternate black and
brightly-coloured stripes on each side. The rays which bend round the
wire in two streams are of equal lengths in the middle stripe; it is
consequently doubly bright from their combined effect; but the rays
which fall on the paper on each side of the bright stripe, being of such
unequal lengths as to destroy one another, form black lines. On each
side of these black lines the rays are again of such lengths as to
combine to form bright stripes, and so on alternately till the light is
too faint to be visible. When any homogeneous light is used, such as
red, the alternations are only black and red; but on account of the
heterogeneous nature of white light, the black lines alternate with
vivid stripes or fringes of prismatic colours, arising from the
superposition of systems of alternate black lines and lines of each
homogeneous colour. That the alternation of black lines and coloured
fringes actually does arise from the mixture of the two streams of light
which flow round the wire, is proved by their vanishing the instant one
of the streams is interrupted. It may therefore be concluded, as often
as these stripes of light and darkness occur, that they are owing to the
rays combining at certain intervals to produce a joint effect, and at
others to extinguish one another. Now it is contrary to all our ideas of
matter to suppose that two particles of it should annihilate one another
under any circumstances whatever; while, on the contrary, two opposing
motions may; and it is impossible not to be struck with the perfect
similarity between the interferences of small undulations of air or of
water and the preceding phenomena. The analogy is indeed so perfect,
that philosophers of the highest authority concur in the belief that the
celestial regions are filled with an extremely rare and highly elastic
medium or ether, whose particles are capable of receiving the vibrations
communicated to them by self-luminous bodies, and of transmitting them
to the optic nerves, so as to produce the sensation of light. The
acceleration in the mean motion of Encke’s comet, as well as of the
comet discovered by M. Biela, renders the existence of such a medium
certain. It is clear that, in this hypothesis, the alternate stripes of
light and darkness are entirely the effect of the interference of the
undulations; for, by actual measurement, the length of a wave of the
mean red rays of the solar spectrum is equal to the 0·0000258th part of
an inch; consequently, when the elevations of the waves combine, they
produce double the intensity of light that each would do singly; and
when half a wave combines with a whole—that is, when the hollow of one
wave is filled up by the elevation of another—darkness is the result. At
intermediate points between these extremes, the intensity of the light
corresponds to intermediate differences in the lengths of the rays.
The theory of interferences is a particular case of the general
mechanical law of the superposition of small motions; whence it appears
that the disturbance of a particle of an elastic medium, produced by two
co-existent undulations, is the sum of the disturbances which each
undulation would produce separately; consequently, the particle will
move in the diagonal of a parallelogram, whose sides are the two
undulations. If, therefore, the two undulations agree in direction, or
nearly so, the resulting motion will be very nearly equal to their sum,
and in the same direction; if they nearly oppose one another, the
resulting motion will be nearly equal to their difference; and, if the
undulations be equal and opposite, the resultant will be zero, and the
particle will remain at rest.
The preceding experiments, and the inferences deduced from them, which
have led to the establishment of the doctrine of the undulations of
light, are the most splendid memorials of our illustrious countryman Dr.
Thomas Young, though Huygens was the first to originate the idea.
It is supposed that the particles of luminous bodies are in a state of
perpetual agitation, and that they possess the property of exciting
regular vibrations in the molecules of the ethereal medium,
corresponding to the vibrations of their own molecules; and that, on
account of its elastic nature, one particle of the ether when set in
motion communicates its vibrations to those adjacent, which in
succession transmit them to those farther off; so that the primitive
impulse is transferred from particle to particle, and the undulating
motion darts through ether like a wave in water; so that light is
motion, and therefore subject to the laws of dynamics and mathematical
analysis. Although the progressive motion of light is known by
experience to be uniform and in a straight line, the vibrations of the
particles are always at right angles to the direction of the ray. The
propagation of light is like the spreading of waves in water; but, if
one ray alone be considered, its motion may be conceived by supposing a
rope of indefinite length stretched horizontally, one end of which is
held in the hand. If it be agitated to and fro at regular intervals,
with a motion perpendicular to its length, a series of similar and equal
tremors or waves will be propagated along it; and if the regular
impulses be given in a variety of planes, as up and down, from right to
left, and also in oblique directions, the successive undulations will
take place in every possible plane. An analogous motion in the ether,
when communicated to the optic nerves, would produce the sensation of
common light. It is evident that the waves which flow from end to end of
the cord in a serpentine form are altogether different from the
perpendicular vibratory motion of each particle of the rope, which never
deviates far from a state of rest. So, in ether, each particle vibrates
perpendicularly to the direction of the ray; but these vibrations are
totally different from and independent of the undulations which are
transmitted through it, in the same manner as the vibrations of each
particular ear of corn are independent of the waves that rush from end
to end of a harvest-field when agitated by the wind.
The intensity of light depends upon the amplitude or extent of the
vibrations of the particles of ether, while its colour depends upon
their frequency. The time of the vibration of a particle of ether is, by
theory, as the length of a wave directly, and inversely as its velocity.
Now, as the velocity of light is known to be 190,000 miles in a second,
if the lengths of the waves of the different coloured rays could be
measured, the number of vibrations in a second corresponding to each
could be computed. That has been accomplished as follows:—All
transparent substances of a certain thickness, with parallel surfaces,
reflect and transmit white light; but, if they be extremely thin, both
the reflected and transmitted light is coloured. The vivid hues on
soap-bubbles, the iridescent colours produced by heat on polished steel
and copper, the fringes of colour between the laminæ of Iceland spar and
sulphate of lime, all consist of a succession of hues disposed in the
same order, totally independent of the colour of the substance, and
determined solely by its greater or less thickness—a circumstance which
affords the means of ascertaining the length of the waves of each
coloured ray, and the frequency of the vibrations of the particles
producing them. If a plate of glass be laid upon a lens of almost
imperceptible curvature, before an open window, when they are pressed
together a black spot will be seen in the point of contact, surrounded
by seven rings of vivid colours, all differing from one another
(N. 199). In the first ring, estimated from the black spot, the colours
succeed each other in the following order:—black, very faint blue,
brilliant white, yellow, orange, and red. They are quite different in
the other rings, and in the seventh the only colours are pale bluish
green and very pale pink. That these rings are formed between the two
surfaces in apparent contact may be proved by laying a prism on the lens
instead of the plate of glass, and viewing the rings through the
inclined side of it that is next to the eye, which arrangement prevents
the light reflected from the upper surface mixing with that from the
surfaces in contact, so that the intervals between the rings appear
perfectly black—one of the strongest circumstances in favour of the
undulatory theory; for, although the phenomena of the rings can be
explained by either hypothesis, there is this material difference, that,
according to the undulatory theory, the intervals between the rings
ought to be absolutely black, which is confirmed by experiment; whereas,
by the doctrine of emanation, they ought to be half illuminated, which
is not found to be the case. M. Fresnel, whose opinion is of the first
authority, thought this test conclusive. It may therefore be concluded
that the rings arise entirely from the interference of the rays: the
light reflected from each of the surfaces in apparent contact reaches
the eye by paths of different lengths, and produces coloured and dark
rings alternately, according as the reflected waves coincide or destroy
one another. The breadths of the rings are unequal; they decrease in
width, and the colours become more crowded, as they recede from the
centre. Coloured rings are also produced by transmitting light through
the same apparatus; but the colours are less vivid, and are
complementary to those reflected, consequently the central spot is
white.
The size of the rings increases with the obliquity of the incident
light, the same colour requiring a greater thickness or space between
the glasses to produce it than when the light falls perpendicularly upon
them. Now, if the apparatus be placed in homogeneous instead of white
light, the rings will all be of the same colour with that of the light
employed, that is to say, if the light be red, the rings will be red,
divided by black intervals. The size of the rings varies with the colour
of the light. They are largest in red, and decrease in magnitude with
the succeeding prismatic colours, being smallest in violet light.
Since one of the glasses is plane and the other spherical, it is evident
that from the point of contact the space between them gradually
increases in thickness all round, so that a certain thickness of air
corresponds to each colour, which in the undulatory system measures the
length of the wave producing it (N. 200). By actual measurement Sir
Isaac Newton found that the squares of the diameters of the brightest
part of each ring are as the odd numbers, 1, 3, 5, 7, &c.; and that the
squares of the diameters of the darkest parts are as the even numbers,
0, 2, 4, 6, &c. Consequently, the intervals between the glasses at these
points are in the same proportion. If, then, the thickness of the air
corresponding to any one colour could be found, its thickness for all
the others would be known. Now, as Sir Isaac Newton knew the radius of
curvature of the lens, and the actual breadth of the rings in parts of
an inch, it was easy to compute that the thickness of air at the darkest
part of the first ring is the 1/89000 part of an inch, whence all the
others have been deduced. As these intervals determine the length of the
waves on the undulatory hypothesis, it appears that the length of a wave
of the extreme red of the solar spectrum is equal to the 0·0000266th
part of an inch; that the length of a wave of the extreme violet is
equal to the 0·0000167th part of an inch; and, as the time of a
vibration of a particle of ether producing any particular colour is
directly as the length of a wave of that colour, and inversely as the
velocity of light, it follows that the molecules of ether producing the
extreme red of the solar spectrum perform 458 millions of millions of
vibrations in a second; and that those producing the extreme violet
accomplish 727 millions of millions of vibrations in the same time. The
lengths of the waves of the intermediate colours, and the number of
their vibrations, being intermediate between these two, white light,
which consists of all the colours, is consequently a mixture of waves of
all lengths between the limits of the extreme red and violet. The
determination of these minute portions of time and space, both of which
have a real existence, being the actual results of measurement, do as
much honour to the genius of Newton as that of the law of gravitation.
The number of advancing waves of light in an inch is known to be from
37,600 to 59,880, and the number of lateral vibrations is from 458 to
727 billions in a second, but the _extent_ of these lateral vibrations
of the particles of the ethereal medium is not known, though both their
extent and velocity are probably very small compared with the length of
the advancing waves and the velocity of propagation. Colour is
identified with the number of vibrations; but whether reflection,
refraction, absorption, &c., have any relations to the lateral
vibrations, or whether they are dependent in part upon some physical
action of the ethereal medium unknown and unsuspected, are points as yet
undetermined. To ascertain these circumstances, Dr. Faraday instituted a
series of the most refined experiments upon the relation of the minute
particles of metals to the vibrations of light.
Gold acts powerfully on light, and possesses a real transparency,
transmitting green rays when very thin; and being capable of extreme
division by solvents without losing its metallic character, its
particles transmit rays of various colours according to their size;
those that transmit the rose-colour in Bohemian glass are of
inconceivable minuteness. The progressive waves of the ether are so long
compared with the dimensions of the molecules to which gold can be
reduced, that it seemed probable to Dr. Faraday when the latter were
placed in a sunbeam that some effective relation might be discovered
between them and the smaller vibrations of the ethereal medium; in which
case, if reflection, refraction, &c., depended upon such relations,
there was reason to expect that these functions would change sensibly by
the substitution of different sized particles of the gold for one
another. At one time Dr. Faraday hoped he had changed one colour into
another by means of gold, which would have been equivalent to a change
in the number of vibrations; but although he has not yet confirmed that
result, his researches are of the greatest interest.[9]
The phenomenon of the coloured rings takes place _in vacuo_ as well as
in air, which proves that it is the distance between the lenses alone,
and not the air, which produces the colours. However, if water or oil be
put between them, the rings contract, but no other change ensues; and
Newton found that the thickness of different media at which a given tint
is seen is in the inverse ratio of their refractive indices, so that the
thickness of laminæ which could not otherwise be measured may be known
by their colour; and, as the position of the colours in the rings is
invariable, they form a fixed standard of comparison, well known as
Newton’s scale of colours; each tint being estimated according to the
ring to which it belongs from the central spot inclusively. Not only the
periodical colours which have been described, but the colours seen in
thick plates of transparent substances, the variable hues of feathers,
of insects’ wings, mother-of-pearl, and of striated substances, all
depend upon the same principle. To these may be added the coloured
fringes surrounding the shadows of all bodies held in an extremely small
beam of light, and the coloured rings surrounding the small beam itself
when received on a screen.
When a very slender sunbeam, passing through a small pin-hole into a
dark room, is received on a white screen, or plate of ground-glass, at
the distance of a little more than six feet, the spot of light on the
screen is larger than the pin-hole: and, instead of being bounded by
shadow, it is surrounded by a series of coloured rings separated by
obscure intervals. The rings are more distinct in proportion to the
smallness of the beam (N. 201). When the light is white there are seven
rings, which dilate or contract with the distance of the screen from the
hole. As the distance of the screen diminishes, the white central spot
contracts to a point and vanishes; and, on approaching still nearer, the
rings gradually close in upon it, so that the centre assumes
successively the most intense and vivid hues. When the light is
homogeneous—red, for example—the rings are alternately red and black,
and more numerous; and their breadth varies with the colour, being
broadest in red light and narrowest in violet. The tints of the coloured
fringes from white light, and their obliteration after the seventh ring,
arise from the superposition of the different sets of fringes of all the
coloured rays. The shadows of objects are also bordered by coloured
fringes when held in this slender beam of light. If the edge of a knife
or hair, for example, be held in it, the rays, instead of proceeding in
straight lines past its edge, are bent when quite close to it, and
proceed from thence to the screen in curved lines called hyperbolas; so
that the shadow of the object is enlarged, and, instead of being at once
bounded by light, is surrounded or edged with coloured fringes
alternating with black bands, which are more distinct the smaller the
pin-hole (N. 202). The fringes are altogether independent of the form or
density of the object, being the same when it is round or pointed, when
of glass or platinum. When the rays which form the fringes arrive at the
screen, they are of different lengths, in consequence of the curved path
they follow after passing the edge of the object. The waves are
therefore in different phases or states of vibration, and either
conspire to form coloured fringes or destroy one another in the obscure
intervals. The coloured fringes bordering the shadows of objects were
first described by Grimaldi in 1665; but, besides these, he noticed that
there are others within the shadows of slender bodies exposed to a small
sunbeam, a phenomenon which has already been mentioned to have afforded
Dr. Young the means of proving, beyond all controversy, that coloured
rings are produced by the interference of light.
It may be concluded that material substances derive their colours from
two different causes: some from the law of interference, such as
iridescent metals, peacocks’ feathers, &c.; others from the unequal
absorption of the rays of white light, such as vermilion, ultramarine,
blue, or green cloth, flowers, and the greater number of coloured
bodies. The latter phenomena have been considered extremely difficult to
reconcile with the undulatory theory of light, and much discussion has
arisen as to what becomes of the absorbed rays. But that embarrassing
question has been ably answered by Sir John Herschel in a most profound
paper on the Absorption of Light by coloured Media, and cannot be better
given than in his own words. It must, however, be premised, that, as all
transparent bodies are traversed by light, they are presumed to be
permeable to the ether. He says,—“Now, as regards only the general fact
of the obstruction and ultimate extinction of light in its passage
through gross media, if we compare the corpuscular and undulatory
theories, we shall find that the former appeals to our ignorance, the
latter to our knowledge, for its explanation of the absorptive
phenomena. In attempting to explain the extinction of light on the
corpuscular doctrine, we have to account for the light so extinguished
as a material body, which we must not suppose annihilated. It may,
however, be transformed; and among the imponderable agents, heat,
electricity, &c., it may be that we are to search for the light which
has become thus comparatively stagnant. The heating power of the solar
rays gives a _primâ facie_ plausibility to the idea of the
transformation of light into heat by absorption. But, when we come to
examine the matter more nearly, we find it encumbered on all sides with
difficulties. How is it, for instance, that the most luminous rays are
not the most calorific, but that, on the contrary, the calorific energy
accompanies, in its greatest intensity, rays which possess comparatively
feeble illuminating powers? These and other questions of a similar
nature may perhaps admit of answer in a more advanced state of our
knowledge; but at present there is none obvious. It is not without
reason, therefore, that the question, ‘What becomes of light?’ which
appears to have been agitated among the photologists of the last
century, has been regarded as one of considerable importance as well as
obscurity by the corpuscular philosophers. On the other hand, the answer
to this question, afforded by the undulatory theory of light, is simple
and distinct. The question, ‘What becomes of light?’ merges in the more
general one, ‘What becomes of motion?’ And the answer, on dynamical
principles, is, that it continues for ever. No motion is, strictly
speaking, annihilated; but it may be divided, and the divided parts made
to oppose and _in effect_ destroy one another. A body struck, however
perfectly elastic, vibrates for a time, and then appears to sink into
its original repose. But this apparent rest (even abstracting from the
inquiry that part of the motion which may be conveyed away by the
ambient air) is nothing else than a state of subdivided and mutually
destroying motion, in which every molecule continues to be agitated by
an indefinite multitude of internally reflected waves, propagated
through it in every possible direction, from every point in its surface
on which they successively impinge. The superposition of such waves
will, it is easily seen, at length operate their mutual destruction,
which will be the more complete the more irregular the figure of the
body, and the greater the number of internal reflections.” Thus Sir John
Herschel, by referring the absorption of light to the subdivision and
mutual destruction of the vibrations of ether in the interior of bodies,
brings another class of phenomena under the laws of the undulatory
theory.
According to Mr. Rankin’s hypothesis of Molecular Vortices[10] the
absorption of light and radiant heat consists in the transference of
motion from the molecules to their atmospheres, and conversely the
emission of light and radiant heat is the transmission of motion from
the atmospheres to the molecules. The great velocity of light and heat
is a natural consequence of this hypothesis, according to which the
vibratory masses must be extremely small compared with the forces
exerted by them.
The ethereal medium pervading space is supposed to penetrate all
material substances, occupying the interstices between their molecules;
but in the interior of refracting media it exists in a state of less
elasticity compared with its density _in vacuo_; and, the more
refractive the medium, the less the elasticity of the ether within it.
Hence the waves of light are transmitted with less velocity in such
media as glass and water than in the external ether. As soon as a ray of
light reaches the surface of a diaphanous reflecting substance, for
example a plate of glass, it communicates its undulations to the ether
next in contact with the surface, which thus becomes a new centre of
motion, and two hemispherical waves are propagated from each point of
this surface; one of which proceeds forward into the interior of the
glass, with a less velocity than the incident waves; and the other is
transmitted back into the air, with a velocity equal to that with which
it came (N. 203). Thus, when refracted, the light moves with a different
velocity without and within the glass; when reflected, the ray comes and
goes with the same velocity. The particles of ether without the glass,
which communicate their motions to the particles of the dense and less
elastic ether within it, are analogous to small elastic balls striking
large ones; for some of the motion will be communicated to the large
balls, and the small ones will be reflected. The first would cause the
refracted wave, and the last the reflected. Conversely, when the light
passes from glass to air, the action is similar to large balls striking
small ones. The small balls receive a motion which would cause the
refracted ray, and the part of the motion retained by the large ones
would occasion the reflected wave; so that, when light passes through a
plate of glass or of any other medium differing in density from the air,
there is a reflection at both surfaces; but this difference exists
between the two reflections, that one is caused by a vibration in the
same direction with that of the incident ray, and the other by a
vibration in the opposite direction.
A single wave of air or ether would not produce the sensation of sound
or light. In order to excite vision, the vibrations of the molecules of
ether must be regular, periodical, and very often repeated: and, as the
ear continues to be agitated for a short time after the impulse by which
alone a sound becomes continuous, so also the fibres of the retina,
according to M. d’Arcet, continue to vibrate for about the eighth part
of a second after the exciting cause has ceased. The interval of time
during which the impression lasts is longer for the blue than for red or
white light: it must not be less than 0ʺ·34. Every one must have
observed, when a strong impression is made by a bright light, that an
object remains visible for a short time after shutting the eyes, which
is supposed to be in consequence of the continued vibrations of the
fibres of the retina. Occasionally the retina becomes insensible to
feebly illuminated objects when continuously presented. If the eye be
turned aside for a moment, the object becomes again visible. It is
probably on this account that the owl makes so peculiar a motion with
its head when looking at objects in the twilight. It is quite possible
that many vibrations may be excited in the ethereal medium incapable of
producing undulations in the fibres of the human retina, which yet have
a powerful effect on those of other animals or of insects. Such may
receive luminous impressions of which we are totally unconscious, and at
the same time they may be insensible to the light and colours which
affect our eyes, their perceptions beginning where ours end.